Difference between revisions of "Construction of transverse common tangent"

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__FORCETOC__
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The transverse common tangents also meet on the line of centres and divide it internally in the ratio of the radii.
=Activity No # 1 - Transverse Common Tangent=
 
  
==Estimated Time==
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===Objectives===
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To construct transverse common tangents for the given circles.
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===Estimated Time===
 
45 minutes
 
45 minutes
==Materials/ Resources needed==
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# Laptop, geogebra file, projector and a pointer.
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===Prerequisites/Instructions, prior preparations, if any===
# Students' individual construction materials.
 
==Prerequisites/Instructions, if any==
 
 
# The students should have prior knowledge of a circle , tangent and direct and transverse common tangents .
 
# The students should have prior knowledge of a circle , tangent and direct and transverse common tangents .
 
# They should understand that a tangent is always perpendicular to the radius of the circle.
 
# They should understand that a tangent is always perpendicular to the radius of the circle.
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# If the same straight line is a tangent to two or more circles, then it is called a common tangent.
 
# If the same straight line is a tangent to two or more circles, then it is called a common tangent.
 
# If the centres of the circles lie on opposite side of the common tangent, then the tangent is called a transverse common tangent.
 
# If the centres of the circles lie on opposite side of the common tangent, then the tangent is called a transverse common tangent.
# Note: In general,
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===Materials/ Resources needed===
*The two circles are named as C1 and C2
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* Digital: Laptop, geogebra file, projector and a pointer.
* The distance between the centre of two circles is 'd'
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* Non Digital: Students' individual construction materials.
* Radius of one circle is taken as 'R' and other as 'r'
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* Gegebra file:
* The length of tangent is 't'
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==Multimedia resources==
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===Process (How to do the activity)===
Laptop
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Note: In general,
==Website interactives/ links/ simulations/ Geogebra Applets==
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# The two circles are named as C1 and C2
<ggb_applet width="1280" height="600" version="4.0" 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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
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# The distance between the centre of two circles is 'd'
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# Radius of one circle is taken as 'R' and other as 'r'
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# The length of tangent is 't'
  
==Process (How to do the activity)==
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The teacher can explain the step by step construction of Transverse common tangent.
# The teacher can explain the step by step construction of Transverse common tangent.  
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* __FORCETOC__ Developmental Questions (What discussion questions)
==Developmental Questions (What discussion questions)==
 
 
# What is a transverse common tangent ?
 
# What is a transverse common tangent ?
 
# What is the radius of the third circle ?
 
# What is the radius of the third circle ?
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# Name the transverse common tangents .
 
# Name the transverse common tangents .
 
# At what points is the tangent touching the circles ?
 
# At what points is the tangent touching the circles ?
==Evaluation (Questions for assessment of the child)==
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* Evaluation (Questions for assessment of the child)
 
# Is the student able to comprehend the sequence of steps in constructing the tangent.
 
# Is the student able to comprehend the sequence of steps in constructing the tangent.
 
# Is the student able to identify error areas while constructing ?
 
# Is the student able to identify error areas while constructing ?
 
# Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?
 
# Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?
 
# Is the student able to understand the difference in the construction protocol between direct common tangent and transverse common tangent ?  
 
# Is the student able to understand the difference in the construction protocol between direct common tangent and transverse common tangent ?  
==Question Corner==
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* Question Corner
 
# What is the formula to find the length of transverse common tangent ?
 
# What is the formula to find the length of transverse common tangent ?
 
# Can a direct common tangent be drawn to two circles one inside the other ?   
 
# Can a direct common tangent be drawn to two circles one inside the other ?   
 
# What are properties of transverse common tangents ?
 
# What are properties of transverse common tangents ?
  
==Activity Keywords==
+
[[Category:Circles]]
#Geogebra
 
#Transverse common tangent
 
 
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Back]
 

Latest revision as of 11:59, 30 October 2019

The transverse common tangents also meet on the line of centres and divide it internally in the ratio of the radii.

Objectives

To construct transverse common tangents for the given circles.

Estimated Time

45 minutes

Prerequisites/Instructions, prior preparations, if any

  1. The students should have prior knowledge of a circle , tangent and direct and transverse common tangents .
  2. They should understand that a tangent is always perpendicular to the radius of the circle.
  3. They should know construction of a tangent to a given point.
  4. If the same straight line is a tangent to two or more circles, then it is called a common tangent.
  5. If the centres of the circles lie on opposite side of the common tangent, then the tangent is called a transverse common tangent.

Materials/ Resources needed

  • Digital: Laptop, geogebra file, projector and a pointer.
  • Non Digital: Students' individual construction materials.
  • Gegebra file:

Process (How to do the activity)

Note: In general,

  1. The two circles are named as C1 and C2
  2. The distance between the centre of two circles is 'd'
  3. Radius of one circle is taken as 'R' and other as 'r'
  4. The length of tangent is 't'

The teacher can explain the step by step construction of Transverse common tangent.

  • Developmental Questions (What discussion questions)
  1. What is a transverse common tangent ?
  2. What is the radius of the third circle ?
  3. What is the difference in finding the radius of the third circle in constructing Dct and that of Tct ?
  4. Why was a third circle constructed ?
  5. Let us try to construct transverse common tangent without the third circle and see.
  6. Name the transverse common tangents .
  7. At what points is the tangent touching the circles ?
  • Evaluation (Questions for assessment of the child)
  1. Is the student able to comprehend the sequence of steps in constructing the tangent.
  2. Is the student able to identify error areas while constructing ?
  3. Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?
  4. Is the student able to understand the difference in the construction protocol between direct common tangent and transverse common tangent ?
  • Question Corner
  1. What is the formula to find the length of transverse common tangent ?
  2. Can a direct common tangent be drawn to two circles one inside the other ?
  3. What are properties of transverse common tangents ?